手法を比較

	頑健回帰	Lasso回帰	最小二乗法 (OLS) 回帰	分位点回帰
分野	統計学	機械学習	計量経済学	計量経済学
系統	Regression model	Machine learning	Regression model	Regression model
提唱年	1964	1996	2019	1978
提唱者	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)	Tibshirani, R.	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
種類	Regression with outlier resistance	Regularized linear regression (L1 penalty)	Linear regression	Conditional quantile regression
原典	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.	Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
別名	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation	LASSO Regresyonu, lasso, L1-regularized regression, L1 regularization	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	conditional quantile regression, regression quantiles, Kantil Regresyon
関連	6	4	5	5
概要	Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.	Lasso regression, introduced by Robert Tibshirani in 1996, is a linear regression method that adds an L1 penalty to the loss so that it shrinks coefficients and performs variable selection at the same time, producing a sparse model. By driving some coefficients exactly to zero it keeps only the predictors that matter.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.